Question: Solve for $x$ and $y$ using elimination. ${3x+4y = 46}$ ${-3x-3y = -36}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {3x+4y = 46}\thinspace$ to find $x$ ${3x + 4}{(10)}{= 46}$ $3x+40 = 46$ $3x+40{-40} = 46{-40}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 10}$ into $\thinspace {-3x-3y = -36}\thinspace$ and get the same answer for $x$ : ${-3x - 3}{(10)}{= -36}$ ${x = 2}$